Capacitance Calculator

1. Pick what you want to find: parallel-plate capacitance, a series or parallel total, or charge and energy from a capacitance you already know.
2. Fill in the fields that appear. For plates, enter the relative permittivity, the plate area and the gap. For a group, type the capacitor values with commas between them.
3. Add a voltage if you want the charge and the stored energy. Read the capacitance and the working line under the result.

Capacitance is the amount of electric charge a capacitor stores for each volt across it. The formula is C = Q / V. The SI unit is the farad (F), and one farad equals one coulomb per volt.

A capacitor is two conductors separated by an insulator. The insulator is called the dielectric. A battery moves charge from one conductor to the other, and an electric field forms in the gap.

One farad is a very large capacitance. Most parts are rated in microfarads (one millionth of a farad), nanofarads (one billionth) or picofarads (one trillionth). This page writes microfarad as uF.

Capacitance depends on the shape and the dielectric, not on the voltage. It is not the same as resistance, which limits current. Capacitor values are tiny numbers in farads, so the scientific notation calculator helps when you move them into other formulas.

The calculator applies four standard formulas. Each one comes from the definition C = Q / V.

1. Parallel plates. Multiply the relative permittivity k by the vacuum permittivity e0 and the plate area A in square meters. Divide by the gap d in meters.
2. Series. Add the reciprocals: 1 / C = 1 / C1 + 1 / C2 + 1 / C3. The total is always smaller than the smallest capacitor.
3. Parallel. Add the values: C = C1 + C2 + C3.
4. Charge and energy. Q = C x V, and E = 1/2 x C x V x V. Energy also equals 1/2 x Q x V.

The vacuum electric permittivity e0 is the NIST CODATA 2022 value. Its relative uncertainty is 1.6 parts in ten billion, so it does not limit your answer. The relative permittivity k is the number that changes with the material.

These are representative room-temperature values from OpenStax University Physics, Table 8.1. A real material varies with grade, temperature and frequency, so use the data sheet value when you have one.

Air-gap plates. Two plates of 100 cm2 (0.01 m2) sit 1 mm apart with k = 1. C = 1 x 8.8541878188e-12 x 0.01 / 0.001 = 88.54 pF. At 12 V the plates hold 1.0625 nC and 6.375 nJ. The field is 0.012 MV/m, far below the limit for air.

Paper dielectric. Put paper with k = 3.7 in the same gap. The capacitance rises 3.7 times to 327.6 pF.

Series group. Capacitors of 1 uF, 5 uF and 8 uF in series give 1 / C = 1 + 0.2 + 0.125 = 1.325 per uF, so C = 0.7547 uF. At 12 V each one holds 9.057 uC. The voltages are 9.06 V, 1.81 V and 1.13 V, which add up to 12 V. The smallest capacitor takes the most voltage.

Parallel group. The same three in parallel give 1 + 5 + 8 = 14 uF. At 12 V they hold 168 uC and 1.008 mJ in total.

Power supply capacitor. A 470 uF capacitor at 12 V holds Q = 470e-6 x 12 = 5.64 mC. The energy is 0.5 x 470e-6 x 144 = 33.84 mJ.

Three things set the capacitance of a parallel-plate capacitor: plate area, gap and dielectric.

Plate Area

Capacitance is proportional to area. Doubling the overlapping area doubles the capacitance. Only the area where the plates face each other counts.

Gap Between the Plates

Capacitance is inversely proportional to the gap. Halving the gap doubles the capacitance. A thinner gap also raises the field, so the voltage limit drops.

Dielectric Material

A dielectric multiplies the vacuum value by k. Paper at 3.7 stores 3.7 times the charge of the same plates in a vacuum at the same voltage.

Voltage Does Not Change Capacitance

For an ideal capacitor, voltage changes the charge and the energy only. Energy rises with the square of the voltage. A 100 uF capacitor holds 1.25 mJ at 5 V and 5 mJ at 10 V, four times as much.

Dielectric Strength

Every insulator breaks down above a certain field. Dry air breaks down near 3.0 MV/m, so a 1 mm air gap fails at about 3 kV. The calculator flags an air gap above that field.

Parallel capacitors add like bigger plates, and series capacitors combine like a wider gap.

These rules are the reverse of the rules for resistors. Resistors add in series, while capacitors add in parallel.

Physics Homework and Lab Reports

Check a parallel-plate answer, or compare a measured value with the ideal one. The percent error calculator gives the gap between the two as a percentage.

Building a Value from Parts You Have

Combine capacitors from a parts drawer to reach a value you do not have. Two 10 uF parts give 20 uF in parallel or 5 uF in series.

Sizing Stored Energy

Find the energy a capacitor holds at its working voltage, for a flash, a hold-up circuit or a discharge resistor. Compare joules with moving objects using the kinetic energy calculator.

1. Mixing Units

The formula needs square meters and meters. An area in square centimeters entered as square meters is wrong by a factor of 10,000. The unit menus convert for you.

2. Swapping the Series and Parallel Rules

Capacitors add in parallel, not in series. Using the resistor rule gives 14 uF where the true series value is 0.7547 uF.

3. Forgetting That Energy Uses Voltage Squared

Doubling the voltage doubles the charge but multiplies the energy by four.

4. Using Absolute Permittivity as K

The k field is the relative value, such as 3.7 for paper. Do not type 32.8 pF/m there. The calculator multiplies k by e0 itself.

5. Treating the Ideal Value as the Real Part

A real capacitor has a tolerance printed on it or in its data sheet. The ideal formula also ignores the fringing field at the plate edges.

6. Handling a Charged Capacitor

A capacitor can stay charged after the power is off. A 330 uF capacitor at 300 V holds 14.85 J. Discharge it safely before you touch it.

The arithmetic is exact for ideal capacitors. Real parts differ because of edge effects, tolerance and material changes.

The definition is C = Q / V, charge divided by voltage. For two parallel plates it becomes C = k x e0 x A / d, where A is the plate area and d is the gap.

The vacuum electric permittivity is 8.8541878188e-12 farads per meter. That is the 2022 CODATA value listed by NIST, often rounded to 8.85e-12 F/m in textbooks.

Add the reciprocals and then invert the sum. Capacitors of 1, 5 and 8 uF in series give 0.7547 uF, which is less than the smallest one.

Add the values. Capacitors of 1, 5 and 8 uF in parallel give 14 uF.

The energy is one half times capacitance times voltage squared. A 470 uF capacitor at 12 V stores 33.84 millijoules.

One farad stores one coulomb at just one volt, which is a great deal of charge. Two plates of one square meter, 1 mm apart in air, give only 8.85 nF.

Yes. A dielectric multiplies the vacuum capacitance by its relative permittivity. Paper, with k = 3.7, raises 88.54 pF to 327.6 pF.

uF is a plain-text way to write microfarad, one millionth of a farad. One uF equals 1,000 nF or 1,000,000 pF.

No. It fits flat plates with a small gap. Cylindrical and spherical capacitors need their own formulas, but Q = C x V and the energy formula work for every capacitor.

No. The calculation runs in your browser and nothing is sent to our servers. Anything you choose to Save stays in this browser only.

• Vacuum electric permittivity, 2022 CODATA recommended value (NIST).
• Capacitors and capacitance: definition, farad and the parallel-plate formula (OpenStax University Physics Volume 2, section 8.1).
• Capacitors in series and in parallel (OpenStax University Physics Volume 2, section 8.2).
• Energy stored in a capacitor (OpenStax University Physics Volume 2, section 8.3).
• Dielectric constants and dielectric strengths, Table 8.1 (OpenStax University Physics Volume 2, section 8.5).